Usually, we study the behavior of the
markets using the traditional supply and demand
framework. Through the use of supply and demand, we
have determined the equilibrium price and equilibrium
quantity in different types of markets. This type of
analysis of market conditions is called partial equilibrium analysis
where we look at the determinants of price and quantity
in a particular market holding all other markets
constant.

A natural extension to the above type of
analysis is general equilibrium
analysis or how demand and supply conditions
interact in several markets to determine the price of
many goods. A common tool in general equilibrium analysis
is the Edgeworth box which
allows the study of the interaction of two individuals
trading two different commodities. This type of analysis
draws on the use of indifference curve analysis to
analyze this trading behavior.

The lower left-hand
corner represents the origin for consumer
'A' and the upper right-hand corner
represents the origin for consumer 'B'. Person A's preferences
(indifference curves) are convex to the origin OA.
Person B's preferences are convex to OB.

Moving to the right means that person
'A' has more of commodity 'X' and person 'B' has less of
that commodity. Moving upwards means that person 'A' has
more of commodity 'Y' and person 'B' has less. Moving in
the northeast direction makes person 'A' better off.
Moving in the southwest direction makes person 'B' better
off.

Rather than introduce budget lines for the two
consumers, the Edgeworth box uses the concept of initial
endowments. An initial endowment 'w' represents
the amount of commodities X & Y individuals A & B
have available before trade. Thus (XA ,YA
) = wA and (XB , YB
) = wB where wA and wB
represents A's and B's initial endowments (or income).
The height of the Edgeworth box represents the total
amount of commodity 'Y' available and the width of the
Edgeworth box represents the total amount of commodity
'X' available. In the absence of any production, the
dimensions of the box remain constant.

One goal of general equilibrium analysis
is to determine if it is possible to make individual 'A'
and/or individual 'B' better off through the
process of exchange given their initial endowments. For
example a trade such that these two individuals move to
point 'R' in the diagram below would make person 'B'
better-off with out harm to 'A':

Any trade that puts
these two individuals into, or on the border of,
the shaded area will make one or both individuals
better off. This is known as a Pareto
Improvement. As long as any Pareto
Improvements remain, an incentive for trade
exists between these two agents.

An optimal allocation of
commodities is determined by the concept of Pareto optimality. A Pareto
optimal allocation of commodities is that allocation
where it is not possible to make one person
better off without making any other person worse off.
This is shown graphically in the diagram below where the
indifference curves of person 'A' are just tangent to
person 'B' as occurs at point 'T'.

If, for example, the
two consumers are at the initial endowment point
'w', it is possible to make person 'B'
better off by moving to point 'R' without making
person 'A' worse off (a movement along person A's
indifference curve). A second trade could be the
movement towards point 'T' which would make
person 'A' better off without making person 'B'
worse off. This trade (from w to T)
would make both person 'A' and person 'B' better
off.

You might remember that the slope of an
indifference curve dy/dx is just the ratio of the
marginal utilities of goods 'X' & 'Y' (or: dy/dx = MUx
/ MUy = MRSxy) thus the condition
for Pareto optimality
may be properly defined as that point where:

MRSA
= MRSB .

The next step in general equilibrium analysis is the
determination of how this movement actually takes place
from the initial endowment to a Pareto efficient
allocation. This movement is acomplished through the
price system where the relative
prices between goods 'X' & 'Y' represent
the terms of trade between the two individuals. The slope
of any line passing through the endowment point
represents this price ratio of commodity X and commodity
Y. Thus if that line is relatively steep, commodity X is
relatively more expensive than commodity Y. If the line
is relatively flat, then the opposite is true.

Through some hypothesized auction process
(where different price ratios are called out), a
market or competitive equilibrium will be established at
that point (a Pareto Optimum), where: